If a line makes an angle of $\pi /4$ with the positive direction of both the $x$-axis and $y$-axis,what angle does it make with the positive direction of the $z$-axis?

If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the positive $X$-axis and positive $Y$-axis respectively,then the angle made by $L$ with the positive direction of $Z$-axis is

Find the angle between the lines whose direction ratios are $1, 1, 2$ and $\sqrt{3}-1, -\sqrt{3}-1, 4$. (in $^{\circ}$)

The coordinates of the point $P$ are $(x, y, z)$ and the direction cosines of the line $OP$ where $O$ is the origin $(0, 0, 0)$ are $l, m, n$. If $r$ is the distance $OP$,then which of the following relations is correct?

If the direction cosines of the two lines satisfy the equations $l+m+n=0$ and $2lm+2ln-mn=0$, then the acute angle between these lines is

If a directed line makes angles $45^{\circ}$ and $60^{\circ}$ with the $X$ and $Y$-axes respectively,then the obtuse angle $\theta$ made by the line with the $Z$-axis is (in $^{\circ}$)